Kinetic theory of transport for inhomogeneous electron fluids
Kinetic theory of transport for inhomogeneous electron fluids
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DOI：
10.1103/physrevb.97.045105
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发表时间：
2018-01-05
影响因子：
3.7
通讯作者：
Hartnoll, Sean A.
中科院分区：
文献类型：
--
作者：
Lucas, Andrew;Hartnoll, Sean A.
电子相互作用和无序之间的相互作用在传统的玻尔兹曼输运理论中被忽略，但在确定非常规金属的电阻率方面可以发挥重要作用。当准粒子寿命较长时，人们可以通过求解空间非齐次玻尔兹曼方程来解释这些相互交织的效应。假设平滑无序并忽略 umklapp 散射，我们求解这些非齐次动力学方程并计算弹道到流体动力学转变的电阻率。电子-电子相互作用的一个重要结果是动量弛豫时间的改变。在同质理论中忽略了这种效应。我们精确地描述了相互作用何时增强动量散射率以及何时降低动量散射率。我们的方法统一了现有的半经典输运理论，并解释了电阻率如何与没有巴伯散射的动量守恒碰撞率成正比。我们将此结果与现有的输运奥秘进行了比较，包括许多费米液体的无序无关 T-2 电阻率，以及许多奇怪金属的 T 线性“普朗克极限”电阻率。
The interplay between electronic interactions and disorder is neglected in the conventional Boltzmann theory of transport, yet can play an essential role in determining the resistivity of unconventional metals. When quasiparticles are long lived, one can account for these intertwined effects by solving spatially inhomogeneous Boltzmann equations. Assuming smooth disorder and neglecting umklapp scattering, we solve these inhomogeneous kinetic equations and compute the electrical resistivity across the ballistic-to-hydrodynamic transition. An important consequence of electron-electron interactions is the modification of the momentum-relaxation time; this effect is ignored in the homogeneous theory. We characterize precisely when interactions enhance the momentum scattering rate, and when they decrease it. Our approach unifies existing semiclassical theories of transport, and explains how the resistivity can be proportional to the rate of momentum-conserving collisions without Baber scattering. We compare this result with existing transport mysteries, including the disorder-independent T-2 resistivity of many Fermi liquids, and the linear-in-T "Planckian-limited" resistivity of many strange metals.